Improved human greenspace exposure equality during 21st century urbanization

Greenspace plays a crucial role in urban ecosystems and has been recognized as a key factor in promoting sustainable and healthy city development. Recent studies have revealed a growing concern about urban greenspace exposure inequality; however, the extent to which urbanization affects human exposure to greenspace and associated inequalities over time remains unclear. Here, we incorporate a Landsat-based 30-meter time-series greenspace mapping and a population-weighted exposure framework to quantify the changes in human exposure to greenspace and associated equality (rather than equity) for 1028 global cities from 2000 to 2018. Results show a substantial increase in physical greenspace coverage and an improvement in human exposure to urban greenspace, leading to a reduction in greenspace exposure inequality over the past two decades. Nevertheless, we observe a contrast in the rate of reduction in greenspace exposure inequality between cities in the Global South and North, with a faster rate of reduction in the Global South, nearly four times that of the Global North. These findings provide valuable insights into the impact of urbanization on urban nature and environmental inequality change and can help inform future city greening efforts.


Supplementary information 1.Calculation of inequality index
In this study, we used three types of widely used measures 1-2 to quantify inequality in human exposure to greenspace, including Lorenz curve-based (i.e., Gini coefficient index), social welfarebased (i.e., Atkinson index), and generalized entropy metrics (i.e., Theil index).To consider the impacts of nearby green environments on the inequality measures, we conducted a buffer analysis on greenspace coverage with a size of 500 m using the image convolution algorithm with the "convolve" function in Google Earth Engine.

Gini index
As shown in Supplementary Fig. 18, the Gini index is calculated by the Lorenz curve framework, and defined as the ratio of the area that lies between the line of equality (i.e., straight diagonal line) and the Lorenz curve (i.e., cumulative share of greenspace exposure ranked by residents that are exposed from lowest to highest greenspace; region A) over the total area under the line of equality (region A plus region B): where   and   represent the areas of regions A and B, respectively.
According to previous studies [3][4] , Gini index can be mathematically formulated as: where   is the greenspace coverage that exposed to j th resident with a buffer size of d (500 m) and N is the number of total residents within the target city.

Atkinson index
The Atkinson index is another inequality metric based on the concept of welfare equivalent equally distributed greenspace, which is defined as the percentage of total greenspace for one society that must forego to have more equal shares of greenspace among individuals in that society 2 .The advantage of the Atkinson index is that it can provide a complete ranking of greenspace distribution in the explicitly social welfare function.Mathematically, the Atkinson index can be calculated as: where ̅ represents the average greenspace exposure and  is the inequality aversion parameter that regulates the sensitivity of the social welfare losses from inequality to greenspace exposure inequality.As  increases, the Atkinson index is more sensitive to changes in the lower end of the greenspace distribution and vice versa.

Theil index
The Theil index is another generalized entropy indicator that measures the ranking greenspace inequality that can overcome the limitation of the Gini index when the Lorenz curves of the two target cities cross 2 .It is defined as:

Supplementary Fig. 2 .
Sensitivity of threshold in the linear unmixing-based greenspace classification to the temporal changes of physical greenspace coverage (GC) for global 1028 cities from 2000-2018.a and b.Threshold = 0.3.c and d.Threshold = 0.4.e and f.Threshold = 0.5.First column is the city-level temporal trend of GC changes (a, c, and e).Second column is the mean annual GC dynamics for Global North and Global South cities (b, d, and f).The nonparametric Theil-Sen slope estimator approach is used to determine the long-term trends of GC.The non-parametric Mann-Kendall is used to evaluate the significance of these detected temporal trends.Large bubble sizes represent a statistically significant level of 0.05 (p-value <0.05) and small bubble sizes represent a non-significant trend with p-value >0.05.The administrative boundaries data is from the Global Administrative Areas (GADM) (https://gadm.org/).Supplementary Fig. 8. Sensitivity of threshold in the linear unmixing-based greenspace classification to the temporal changes of greenspace exposure inequality measured by the Gini index for global 1028 cities from 2000-2018.a and b.Threshold = 0.3.c and d.Threshold = 0.4.e and f.Threshold = 0.5.First column is the city-level temporal trend of Gini changes (a, c, and e).Second column is the mean annual Gini dynamics for Global North and Global South cities (b, d, and f).The non-parametric Theil-Sen slope estimator approach is used to determine the long-term trends of Gini.The non-parametric Mann-Kendall is used to evaluate the significance of these detected temporal trends.Large bubble sizes represent a statistically significant level of 0.05 (p-value <0.05) and small bubble sizes represent a non-significant trend with p-value >0.05.The administrative boundaries data is from the Global Administrative Areas (GADM) (https://gadm.org/).Supplementary Fig. 15.Comparative contributions of greenspace and population to the temporal change in the Gini index using the empirical approach proposed by Tuholske et al. (2020).a-b.Spatial patterns of population versus greenspace for the overall change of the Gini index using the comparative contribution (CC) metric: CC =(|β pop | − |β green |) ÷ |β expo |. c-d.City statistics from greenspace and population to the temporal change in greenspace exposure inequality.In a and c, the overall trend   and the share of greenspace   are first calculated and then the share of population is quantified:   =   −   .In b and d, the overall trend   and the share of population   are first calculated and then the share of greenspace is quantified:   =   −   .The administrative boundaries data is from the Global Administrative Areas (GADM) (https://gadm.org/).

Table S1 .
Statistics of temporal trends of city-level greenspace coverage, human exposure to greenspace, and greenspace exposure inequality across regions.The greenspace coverage is calculated by the spectral unmixing-based threshold classification approach, with a 0.3 threshold.

Table S2 .
Statistics of temporal trends of city-level greenspace coverage, human exposure to greenspace, and greenspace exposure inequality across regions.The greenspace coverage is calculated by the spectral unmixing-based threshold classification approach, with a 0.4 threshold.

Table S3 .
Statistics of temporal trends of city-level greenspace coverage, human exposure to greenspace, and greenspace exposure inequality across regions.The greenspace coverage is calculated by the spectral unmixing-based threshold classification approach, with a 0.5 threshold.

Table S5 .
Statistics of temporal trends of greenspace exposure inequality measured by the Theil index across regions